Opto-electronic arrangement to capture relative movements or relative positions of two objects, and design methodology

ABSTRACT

The invention concerns an opto-electronic arrangement for capturing relative movements or relative positions of two objects, including at least one position-sensitive detector. The opto-electronic arrangement is characterized in that the position-sensitive detector is illuminated by at least two light emission devices, to form two measuring cells with a common detector. The invention also concerns an opto-electronic arrangement to capture relative movements or relative positions of two objects, which can mainly capture only translatory movements. This invention also concerns a force and/or moment sensor, and a pan/zoom sensor with a first plate and a second plate, which are elastically joined to each other and movable relative to each other, characterized by such an opto-electronic arrangement to capture relative movements or relative positions of two objects.

BACKGROUND OF THE INVENTION

The invention concerns an opto-electronic arrangement to capturerelative movements or relative positions of two objects. Thisarrangement includes at least one position-sensitive detector, and eachposition-sensitive detector is illuminated by a light emission device,to form a measuring cell. The invention also concerns a force and/ormoment sensor, which makes use of such an arrangement. Finally, theinvention concerns a PC keyboard which has the force and/or momentsensor according to the invention.

For the computer user, it is becoming increasingly important to controlthree-dimensional movements via a peripheral device. A three-dimensionaldeflection is captured by the peripheral device and described as atranslation (X, Y, Z) and/or a rotation (A, B, C) in space. The mostimportant component is the sensor, which can measure the deflection inup to six (6) degrees of freedom.

PRIOR ART

DE-36 11 337 A1 discloses an opto-electronic arrangement which is housedin a plastic sphere, and can simultaneously capture six components,namely translations along three axes and angular rotations around threeaxes. For this purpose, six light-emitting devices are arranged in oneplane at essentially the same angular distances from each other. Apermanently arranged slotted diaphragm is connected in front of eachlight-emitting device. The relative movements or relative positions aredetected by light-sensitive detectors, which are arranged so that theycan move relative to the arrangement of light-emitting devices andslotted diaphragms, and the detector axis of which runs perpendicularlyto the direction of the slots. The arrangement requires a relatively lowdesign cost, since the light-emitting devices, diaphragms and otherelectronic devices as required for control and analysis can be arrangedusing conventional soldering technology on a single board, which can bepermanently connected to a first object. The position-sensitivedetectors are connected to the second object. However, it isdisadvantageous that the arrangement takes up a relatively large area.The reason is the relatively large spatial extent of the diaphragms anddetectors which are arranged in a ring around the light emissiondevices. This sets a limit to the miniaturisation of the arrangement.

Without any claim to completeness, other documents which show thetechnical background for the invention are: DE-27 27 704 C3, DE-36 11336 C2, DE-32 40 241 A1, U.S. Pat. No. 3,921,445 and U.S. Pat. No.3,628,394.

Problem on Which the Invention is Based

Opto-electronic arrangements to capture relative movements or relativepositions, as well as force and/or moment sensors which use sucharrangements, gained significance in the past mainly in industrialapplications. Examples are control of robots and measurement of forceson motor vehicle test and measuring stands. But commercially veryinteresting application possibilities for the arrangements and sensorsexist mainly in the office sector and entertainment electronics. Herethey have the function of an input device with which up to sixcomponents can be input, in contrast to a joystick, a mouse or atrackball, which in general allow only two components to be input.Simple, convenient input of six components, as is allowed by a forceand/or moment sensor with an opto-electronic arrangement, is desirable,for instance, to control 3D design software and sophisticated computergames. However, input devices until now have been decidedly unwieldybecause of the area/volume which they require, and this was essentiallythe reason they were not more widely used. Miniaturisation would allowthem to be used in, for instance, games consoles, PC keyboards ornotebook computers, and thus make a broad market penetration possible.

The typical 3D input devices are used for view manipulation ofthree-dimensional objects in 6 degrees of freedom simultaneously (6DOF=3 translations and 3 rotations). The cap or sphere of the 3D inputdevice is carried on springs, and allows arbitrary deflection in space(6 DOF). This group of input devices is aimed at customers with true 3Dapplications (6 DOF), such as Catia or other CAD applications.

As well as the true 6 DOF applications, there is also a large group ofapplications in which rotating an object is not desired. Examples ofsuch applications are the Office products (Word, Excel, Powerpoint etc.)and image processing programs (Adobe Photoshop, Acrobat Reader etc.).The manipulated object is usually a two-dimensional master (“paper withwriting or pictures”), and rotating the master is not desired. Thecustomer still wishes to change the view, but only by shifting (pan—2DOF) and enlarging/reducing (zoom—1 DOF) the object.

The aim of development for this customer group is to build an inputdevice which is especially suitable for pan/zoom applications. In thisway, the high cost of a full 3D sensor (6 DOF), in which the threerotational movements are simply ignored, could be saved.

Thus, starting from the prior art, this invention is based on the objectof creating an arrangement for capturing the relative movements orrelative positions of two objects, said arrangement allowing a moremanoeuvrable design compared with known arrangements. For instance, thedesign of the arrangement could be more efficient and/or flexible, orrequire a smaller area. Also, the design of the arrangement could bemore economical and/or be specially suitable for pan/zoom applications.

Additionally, the invention is based on the object of creating a forceand/or moment sensor which also allows a more elegant design incomparison with known sensors. Finally, the invention is based on theobject of creating an input device which is for use in the office andallows uncomplicated input of up to six force or torque components.

Solution According to the Invention

To achieve this object, the invention discloses an opto-electronicarrangement, which is defined by the features of claim 1, 10, 22, 29 or35, to capture relative movements or relative positions of two objects.The invention also discloses a force and/or moment sensor, which isdefined by the features of claim 42. Preferably, the force sensor isused as a pan/zoom sensor for image processing and other similar officeapplications. Finally, it also discloses a personal computer keyboardwhich is defined by the features of claim 53.

Structure and Further Development of the Solution According to theInvention

An opto-electronic arrangement for capturing relative movements orrelative positions of two objects according to one form of the inventionincludes at least one position-sensitive detector, and is characterizedin that the position-sensitive detector is illuminated by at least twolight emission devices, to form two measuring cells with a commondetector.

Preferably, each of the two measuring cells which are formed by a commondetector has a slotted diaphragm which is arranged in the beam path ofthe corresponding light emission device, between the said light emissiondevice and the position-sensitive detector. Each position-sensitivedetector can be associated with two adjacent slotted diaphragms.

In a preferred version of the opto-electronic arrangement, a slotdirection of at least one of the slotted diaphragms is aligneddiagonally in relation to the light-sensitive part of the detector. Inanother preferred version of the opto-electronic arrangement, a lightplane, which shines through at least one of the slotted diaphragms andfalls on the detector, forms an angle with a plane of a light-sensitivepart of the detector.

It is preferred that each detector is illuminated alternately (i.e.periodically) by a light emission device. A measurement value of thedetector is read out simultaneously. In other words, the detector ofeach measuring cell is illuminated by only one light emission device ata particular time, and the measurement value of the detector is read outsimultaneously.

Typically, the measuring cells with the common detector are arrangedsuch that the beam paths which emanate from the light emission devicesintersect and illuminate the same portion of the common detector in theplane of their intersection.

An opto-electronic arrangement according to a further form of theinvention includes at least one position-sensitive detector, which isilluminated by a light emission device, to form a measuring cell, whichalso has a slotted diaphragm which is arranged in the beam path of thelight emission device between the light emission device and theposition-sensitive detector. This opto-electronic arrangement ischaracterized in that a light plane which shines through the slotteddiaphragm and falls on the detector is oriented at an angle in relationto a light-sensitive part of the detector.

In a preferred version of the opto-electronic arrangement, the lightplane forms an angle with a plane of the light-sensitive part of thedetector. Preferably, a slot direction of the slotted diaphragm runsessentially perpendicularly to the light-sensitive part of the detector.

In an alternative version of the opto-electronic arrangement, a slotdirection of the slotted diaphragm is aligned diagonally in relation tothe light-sensitive part of the detector.

In a preferred version of this opto-electronic arrangement of theinvention, the position-sensitive detector is associated with twoadjacent slotted diaphragms, said position-sensitive detector acting aspart of two different measuring cells. Preferably, each slotteddiaphragm is illuminated by its own light emission device, so that eachposition-sensitive detector is illuminated by two light emissiondevices, to form one measuring cell with a common detector.

In a particularly preferred configuration, each of the two adjacentslotted diaphragms is illuminated by a respectively arranged lightemission device. The two adjacent slotted diaphragms can togetherenclose an angle, and can also preferably have slots which are arrangedperpendicularly to each other.

An opto-electronic arrangement to capture relative movements or relativepositions of two objects according to yet another form of the inventionincludes at least one position-sensitive detector, eachposition-sensitive detector being illuminated by its own light emissiondevice, to form a measuring cell. This opto-electronic arrangement ischaracterized in that the measuring cells are arranged in groups, sothat the measuring cells of each group are essentially arranged parallelor perpendicularly to each other.

In a preferred version of this opto-electronic arrangement, themeasuring cells also each include a slotted diaphragm which is arrangedin the beam path of the light emission device between the light emissiondevice and the position-sensitive detector, a detector axis of theposition-sensitive detector being aligned essentially perpendicularly toa slot direction of the slotted diaphragm. The detector axes of theposition-sensitive detectors in each group of measuring cells arepreferably arranged parallel to each other.

According to another form of the invention, an opto-electronicarrangement to capture relative movements or relative positions of twoobjects includes at least two position-sensitive detectors, eachposition-sensitive detector being illuminated by its own light emissiondevice, to form a measuring cell. This opto-electronic arrangement ischaracterized in that all position-sensitive detectors and lightemission devices are arranged in a common plane, and that the measuringcells are arranged parallel to Cartesian axes. The measuring cells cantherefore be arranged essentially parallel to each other and/oressentially perpendicularly to each other.

In a preferred version of this opto-electronic arrangement, themeasuring cells also each include a slotted diaphragm which is arrangedin the beam path of the light emission device between the light emissiondevice and the position-sensitive detector, a detector axis of theposition-sensitive detector being aligned essentially perpendicularly toa slot direction of the slotted diaphragm.

In a preferred version of the opto-electronic arrangement of theinvention, an element of each measuring cell, consisting of lightemission device, slotted diaphragm and detector, is movable relative tothe other two elements. The movable element is preferably arranged inthe centre of rotation of the measuring cell, so that the measuring cellcan generally only (i.e. exclusively) capture translatory movements. Inprinciple, therefore, this measuring cell cannot capture rotationalmovements. Rotations can be captured only if the movable element is at adistance from the centre of rotation. If this distance from the centreof rotation is zero or minimal, the measuring cell is “blind” or “almostblind” to the rotational movement.

According to another form of the invention, an opto-electronicarrangement to capture relative movements or relative positions of twoobjects includes at least one position-sensitive detector, eachposition-sensitive detector being illuminated by a light emissiondevice, to form a measuring cell, and the measuring cell also has aslotted diaphragm which is arranged in the beam path of the lightemission device between the light emission device and theposition-sensitive detector. One element of the measuring cell,consisting of light emission device, slotted diaphragm and detector, ismovable relative to the other two elements, and the measuring cell cancapture exclusively translatory movements. The movable element of themeasuring cell may be arranged in the centre of rotation of themeasuring cell. Preferably, the movable element of each measuring cellis arranged in the centre of rotation of the corresponding measuringcell.

In a preferred version of the opto-electronic arrangement of theinvention, the arrangement includes at least three measuring cells,preferably from three to six measuring cells or even more than sixmeasuring cells.

In a preferred version of the opto-electronic arrangement of theinvention, at least one measuring cell consisting of light emissiondevice, slotted diaphragm and detector is provided with a movable lightemission device, this measuring cell having a greater working range ormovement range.

In a possible extension of the invention, all light emission devices,preferably infra-red light-emitting diodes (ILEDs) andposition-sensitive detectors, preferably position-sensitive infra-reddetectors, are arranged in a common (first) plane.

According to another aspect of the invention, a force and/or momentsensor is provided, which is characterized by an opto-electronicarrangement according to the invention to capture relative movements orrelative positions of two objects. The two objects preferably consist ofa first plate and a second plate, which are elastically joined to eachother and movable relative to each other.

The 3D input devices according to the invention can be equated to aforce and/or moment sensor. The translatory movements (X, Y, Z)correspond to the forces (F_(x), F_(y), F_(z)), and the rotationalmovements (A, B, C) correspond to the moments (M_(x), M_(y), M_(z)). Apan/zoom sensor corresponds to a force sensor (F_(x), F_(y), F_(z)),since the pan/zoom sensor can capture only translatory movements (X, Y,Z).

Other preferred arrangements of the invention are disclosed in theindependent claims and in the following description of embodiments.

BRIEF DESCRIPTION OF DRAWINGS

Embodiments are shown in the following figures. Components withidentical or similar functions are marked with the same referencesymbols.

FIG. 1 shows a measuring cell, consisting of a LED (light-emittingdiode), a diaphragm and a PSD (position sensitivity detector);

FIG. 2 shows the parameters of a measuring cell according to FIG. 1;

FIG. 3 shows the considerations about the intersection plane andidealised intersection point;

FIG. 4 shows a graphic representation of the calculation of atranslatory movement of the diaphragm;

FIGS. 5 a-5 c show possible changes of the parameters of the measuringcell without functional effect;

FIGS. 6 a, 6 b show a measuring cell of an opto-electronic arrangementaccording to the invention, with rotation of the diaphragm about thevector LEDdir;

FIG. 7 shows an opto-electronic arrangement according to the invention,with six measuring cells according to FIGS. 6 a and 6 b;

FIG. 8 shows a measuring cell of an opto-electronic arrangementaccording to the invention, with rotation of the diaphragm about thevector IRISdir;

FIG. 9 shows an opto-electronic arrangement according to the invention,with six measuring cells according to FIG. 8;

FIG. 10 shows an opto-electronic arrangement according to the invention,with three measuring cells, corresponding to three Cartesian axes;

FIGS. 11 a-11 c show the structure of measuring cells of anopto-electronic arrangement according to the invention, multiplemeasuring cells being combined with each other, i.e. the measuring cellshave a common position-sensitive detector;

FIGS. 12 a, 12 b show a variation of the opto-electronic arrangementaccording to FIG. 11 c;

FIGS. 13 a, 13 b show the structure of an opto-electronic arrangementaccording to the invention, which is suitable for measuring six degreesof freedom;

FIGS. 14 a-14 c show the structure of another opto-electronicarrangement according to the invention, which is suitable for measuringsix degrees of freedom;

FIG. 15 shows an opto-electronic arrangement according to the invention,consisting of three pairs of parallel measuring cells;

FIGS. 16 a-16 c show a pair of adjacent diaphragms for anopto-electronic arrangement according to the invention;

FIG. 17 a shows an opto-electronic arrangement according to theinvention, consisting of three pairs of measuring cells which arecombined with each other, and have the diaphragms according to FIGS. 16a-16 c;

FIG. 17 b shows the opto-electronic arrangement according to FIG. 17 a,in which each LED is activated alternately (i.e. periodically);

FIG. 18 shows a graphic representation of the elements of a measuringcell;

FIG. 19 shows a graphic representation to calculate a translatorymovement of the optical element (LED);

FIG. 20 shows a graphic representation to calculate a translatorymovement of the diaphragm;

FIG. 21 shows a graphic representation to calculate a translatorymovement of the position-sensitive detector (PSD);

FIG. 22 shows a further opto-electronic arrangement according to theinvention, consisting of three measuring cells in the same plane.

DETAILED DESCRIPTION OF THE EMBODIMENTS

Optical Sensor

Sensors for capturing a three-dimensional deflection are built up ofoptical elements. The arrangement of a LED (light emittent diode), adiaphragm and a PSD (position sensitivity detector) as the measuringcell of a complete sensor has proved itself. In FIG. 1, a singlemeasuring cell is shown.

A LED emits a light cone, which strikes a slotted diaphragm, and theremaining light plane beyond the diaphragm intersects a one-dimensionalPSD. The intersection point of the light plane with the PSD can bedescribed by a scalar factor λ, which indicates the signed distance ofthe intersection point on the PSD from the resting (initial) position.Subsequently, the factor λ is understood as the determined voltage ofthe PSD. An important property results from the arrangement of the threeoptical elements into a measuring cell. The measuring cell capturesparticular movements (X, Y, Z, A, B or C), and cannot simultaneouslymeasure other movements. Thus each individual measuring cell can be seenas the sensor for particular movements. The sum of all capturedmovements gives the measurement space of the complete sensor.

Parameters of a Measuring Cell

For the precise description of the measuring cell, the positions of theLED, diaphragm and PSD are required. To give the position, in the caseof the LED the source of the generated light is used. In the cases ofthe diaphragm and PSD, the centre of the optical element is used. Thisis not absolutely necessary, but makes the further calculation clearerand has the effect that the scalar factor in the resting position hasthe value λ=0. Additionally, the direction of the slot in the diaphragmand the direction of the position-sensitive area of the PSD arerequired. FIG. 2 shows the necessary positions and directions whichdescribe the measuring cell.

-   LED position of LED-   IRISpos position of diaphragm (centre)-   IRISdir direction of slot in diaphragm-   PSDpos position of PSD (centre)-   PSDdir direction of light-sensitive part of PSD Parameters of the    measuring cell

In the definition of the parameters, some assumptions apply. The lightcone of the LED throws its light on the diaphragm, and the resultinglight plane intersects the PSD in the whole working range.

For the later considerations, it is useful to define the viewingdirection of the LED. It is given by the LED position and diaphragmposition, and by the LED position and PSD position. It is assumed thatthe three points (LED, IRISpos and PSDpos) are arranged so that they arein a straight line.${LEDdir} = {\frac{{IRISpos} - {LED}}{{{IRISpos} - {LED}}} = \frac{{PSDpos} - {LED}}{{{PSDpos} - {LED}}}}$

The vector of the viewing direction LEDdir is standardised to thelength 1. The standardisation to the length 1 also applies to thedirection of the slotted diaphragm and the direction of thelight-sensitive area of the PSD.

The thickness of the slotted diaphragm and of the position-sensitivearea is seen as ideally thin. When the intersection of the light planewith the PSD is idealised, the result is an intersection point, not anintersection plane. The magnitude λ indicates the distance of theintersection point from the resting position. The result is positivevalues for the magnitude λ if the intersection point moves from theresting position in the direction PSDdir, and negative values for theopposite deflection. Obviously, the magnitude λ can be definedarbitrarily differently, and the resting position does not necessarilyhave to be in the centre. A different definition affects thecalculation/working range of the individual measuring cells, but not thebasic function or the arrangement of multiple measuring cells.

In FIG. 3, the considerations about the intersection plane and idealisedintersection point are shown.

Later, the distance of the intersection point from the resting position(magnitude λ) is indicated by a voltage U_(1 . . . 6) of the associatedPSD. The greater the amount of the voltage, the greater is the distanceof the intersection point from the resting position. The sign of thevoltage indicates on which side (PSDdir) of the resting position theintersection point is.

Calculation of the Intersection Point

The measuring cell captures the movement of the three optical elementsrelative to each other. The value λ is determined. It is assumed thatone optical element (LED, diaphragm or PSD) moves, and the other twoelements are in fixed positions. The case of two optical elements movingcan be transferred to the case of one optical element moving, providedthat the movable elements move in the same way (rigidly coupled). Theresult is three different scenarios:Captured Movement $1.\quad\underset{\_}{{LED}\quad{movable}}$$\lambda = \frac{\begin{matrix}{\left\lbrack {{{Rotate} \cdot \left( {{LED} + {Translate}} \right)} - {PSDpos}} \right\rbrack \cdot \left( \left\lbrack {{Rotate} \cdot} \right. \right.} \\\left. {\left. {\left( {{LED} + {Translate}} \right) - {IRISpos}} \right\rbrack \times {IRISdir}} \right)\end{matrix}}{\begin{matrix}{{PSDdir} \cdot \left( \left\lbrack {{Rotate} \cdot \left( {{LED} +} \right.} \right. \right.} \\\left. {\left. {\left. {Translate} \right) - {IRISpos}} \right\rbrack \times {IRISdir}} \right)\end{matrix}}$ $2.\quad\underset{\_}{{Diaphragm}\quad{movable}}$$\lambda = \frac{\begin{matrix}{\left( {{LED} - {PSDpos}} \right) \cdot \left\lbrack \left( {{LED} - {{Rotate} \cdot \left( {{IRISpos} +} \right.}} \right. \right.} \\\left. {\left. \left. {Translate} \right) \right) \times \left( {{Rotate} \cdot {IRISdir}} \right)} \right\rbrack\end{matrix}}{\begin{matrix}{{PSDdir} \cdot \left\lbrack {\left( {{LED} - {{Rotate} \cdot \left( {{IRISpos} + {Translate}} \right)}} \right) \times} \right.} \\\left. \left( {{Rotate} \cdot {IRISdir}} \right) \right\rbrack\end{matrix}}$ $3.\quad\underset{\_}{{PSD}\quad{movable}}$$\lambda = \frac{\begin{matrix}{\left( {{LED} - {{Rotate} \cdot \left( {{PSDpos} + {Translate}} \right)}} \right) \cdot} \\\left\lbrack {\left( {{LED} - {IRISpos}} \right) \times {IRISdir}} \right\rbrack\end{matrix}}{\left( {{Rotate} \cdot {PSDdir}} \right) \cdot \left\lbrack {\left( {{LED} - {IRISpos}} \right) \times {IRISdir}} \right\rbrack}$

The vector Translate indicates the displacement of the movable opticalelement. The matrix Rotate describes the rotation of the movable opticalelement about the co-ordinate origin (e.g. with the roll, pitch, yawangles). In the resting position, the vector Translate is 0 and thematrix Rotate equals the identity matrix.

Calculation of a Translatory Movement

The above equations are further decomposed. The rotational portion istransferred to the translatory portion. A rotational movement can becaptured by the measuring cell only because the rotation also causes adisplacement, because of a lever. FIG. 4 shows an example in which adiaphragm is rotated. The rotation becomes measurable only because ofthe distance of the diaphragm from the centre of rotation (where the LEDis in the example). The measuring cell therefore captures thedisplacements X and Y. The simultaneous rotation of the diaphragmremains ineffective or negligible. In the case of the arrangementspresented here, the magnitude of the rotation is low and limited to afew degrees. The translation (Translate) is thus the dominating factor.

The rotation is “transferred” to the Translate vector, and then alsoincludes the translatory movement which occurs because of the rotationof the movable portion. This translatory portion can occur only if themovable part is not in the centre of rotation. The actual rotation ofthe movable part is ignored. The simplification of the portionRotate*Translate≈Translate is applied.

The relative translatory movement of the movable part of the measuringcell is newly specified, and is thus:

Translate→Rotate·<movableportion>−<movableportion>+Translate

Subject to the condition:

0=IRISdir·(LED×PSDpos−IRISpos×PSDpos+IRISpos×LED)

λ=0 applies to the condition of no deflection (Translation=Rotation=(0 00)^(T)). The following simplifications result for the above equations(E=identity matrix):$\left. {1.\quad\underset{\_}{{LED}\quad{movable}}\text{:}\quad{Translate}}\rightarrow{{Translate} + {\left( {{Rotate} - E} \right){LED}}} \right.$$\lambda = \frac{{Translate}\left\lbrack {\left( {{PSDpos} - {IRISpos}} \right) \times {IRISdir}} \right\rbrack}{\begin{matrix}{{{PSDdir} \cdot \left( {\left\lbrack {{LED} - {IRISpos}} \right\rbrack \times {IRISdir}} \right)} +} \\{{Translate}\left( {{IRISdir} \times {PSDdir}} \right)}\end{matrix}}$$\left. {2.\quad\underset{\_}{{Diaphragm}\quad{movable}}\text{:}\quad{Translate}}\rightarrow{{Translate} + {\left( {{Rotate} - E} \right){IRISpos}}} \right.$$\lambda = \frac{{Translate}\left\lbrack {\left( {{LED} - {PSDpos}} \right) \times {IRISdir}} \right\rbrack}{\begin{matrix}{\left. {\left( {{LED} - {IRISpos}} \right)\left( {{IRISdir} \times {PSDdir}} \right)} \right) -} \\{{Translate}\left( {{IRISdir} \times {PSDdir}} \right)}\end{matrix}}$$\left. {3.\quad\underset{\_}{{PSD}\quad{movable}}\text{:}\quad{Translate}}\rightarrow{{Translate} + {\left( {{Rotate} - E} \right){PSDpos}}} \right.$$\lambda = \frac{- {{Translate}\left( {\left( {{LED} - {IRISpos}} \right) \times {IRISdir}} \right)}}{{PSDdir} \cdot \left( {\left( {{LED} - {IRISpos}} \right) \times {IRISdir}} \right)}$Changes with No Functional Effect on the Measuring Cell

The above equations describe the structure of a measuring cell quitegenerally. Because of the geometrical arrangement, it can be seen thatparameters in the measuring cell can be changed with no change to thefunctioning of the measuring cell. Particular changes to one or moreparameters of the measuring cell are thus insignificant for the actualfunction. The result is an additional “margin” for the arrangement ofthe measuring cell, resulting in a changed geometrical structure, but noeffect on the function of the measuring cell.

In FIG. 5 a, it can be seen that rotation of the PSD by the vectorPSDdir, or rotation by the vector LEDdir×PSDdir, and/or displacementalong the vector LEDdir×PSDdir have no effect as long as light stillfalls on the PSD. If a real PSD prevents light falling, e.g. at arotation of 90°, obviously the measuring cell no longer functions. Untilthis situation occurs, all rotations of the PSD have no functionaleffect on the measuring cell.

In FIG. 5 b, it can be seen that something similar applies to thediaphragm. Rotation of the diaphragm about the vector IRISdir, and/ordisplacement of the diaphragm along the vector IRISdir, or rotationabout the vector IRISdir×LEDdir have no effect on the measuring cell, aslong as light can shine through the slot of the diaphragm.

In FIG. 5 c, it is demonstrated that the LED can be arbitrarily rotatedabout the vector LEDdir. Even rotation about the vectors which areperpendicular to it or displacement along the IRISdir vector is possiblewith no functional effect on the measuring cell, as long as the lightcone of the LED covers the whole working range.

Rotating the Light Plane About the LEDdir Vector

There are other changes to the arrangement of the measuring cell whichaffect its function. In these cases, the usual perpendicular orquasi-perpendicular arrangement is abandoned. The result of rotating thediaphragm about the LEDdir vector is that the light plane strikes thePSD only in a perpendicular or quasi-perpendicular direction. FIGS. 6 aand 6 b show such an arrangement in which the diaphragm has been rotatedby 45°. In FIG. 6 a, the rotation of the slotted diaphragm in relationto the PSD can be seen. FIG. 6 b shows how the light plane falls on thePSD in this case.

In FIG. 7 (movable diaphragm), a complete sensor arrangement, in whicheach diaphragm is rotated by 45°, is shown. In Table 6a, the parametersof all 6 measuring cells are listed. The parameter data is ordered inthe sequence x, y and z with reference to the Cartesian co-ordinatesystem. The parameters ${LED},{IRISpos},{{PSDpos} = \begin{pmatrix}x \\y \\z\end{pmatrix}}$should be understood as points of the individual optical elements, andthe parameters ${IRISdir},{{PSDdir} = \begin{pmatrix}x \\y \\z\end{pmatrix}}$

are the direction vectors of the measuring cell, with the property|IRISdir|=|PSDdir|=1. TABLE 6a 1 2 3 4 5 6 LED +6.0000 +3.0000 −3.0000−6.0000 −3.0000 +3.0000 +0.0000 +0.0000 +0.0000 +0.0000 +0.0000 +0.0000+0.0000 +5.1962 +5.1962 +0.0000 −5.1962 −5.1962 PSDpos +23.0000 +11.5000−11.5000 −23.0000 −11.5000 +11.5000 +0.0000 +0.0000 +0.0000 +0.0000+0.0000 +0.0000 +0.0000 +19.9186 +19.9186 +0.0000 −19.9186 −19.9186PSDdir +0.0000 −0.8660 +0.0000 +0.0000 +0.0000 +0.8660 +1.0000 +0.0000+1.0000 +0.0000 +1.0000 +0.0000 +0.0000 +0.5000 +0.0000 −1.0000 +0.0000+0.5000 IRISpos +20.0000 +10.0000 −10.0000 −20.0000 −10.0000 +10.0000+0.0000 +0.0000 +0.0000 +0.0000 +0.0000 +0.0000 +0.0000 +17.3205+17.3205 +0.0000 −17.3205 −17.3205 IRISdir +0.0000 −0.6124 −0.6124+0.0000 +0.6124 +0.6124 −0.7071 +0.7071 −0.7071 +0.7071 −0.7071 +0.7071+0.7071 +0.3536 −0.3536 −0.7071 −0.3536 +0.3536

TABLE 6b Translation error 3.9%, rotation error 9.1% U1 U2 U3 U4 U5 U6 X+0.0002 −0.2353 −0.2329 −0.0002 +0.2357 +0.2343 Y +0.1373 −0.1404+0.1347 −0.1372 +0.1400 −0.1336 Z +0.2731 +0.1395 −0.1373 −0.2731−0.1390 +0.1352 A −0.0048 +0.6723 −0.6649 +0.0032 +0.6768 −0.6678 B−0.3924 −0.3880 −0.3893 −0.3918 −0.3960 −0.3962 C +0.7902 −0.4153−0.4091 +0.7736 −0.3645 −0.3840Rotating the Light Plane About the IRISdir Vector

A further change to the measuring cell is achieved by rotating the lightplane about the IRISdir vector. FIG. 8 shows a corresponding arrangementin which the LED has been rotated away by 45°.

In FIG. 9 (movable diaphragm), a complete sensor arrangement, in whichall LEDs have been displaced out of the plane arrangement and the lightplanes fall diagonally on the PSDs, is shown. This results in a changeof the measuring cell in the case of the vertically arranged PSDs only.The horizontally arranged PSDs register no change to the measuring cell.TABLE 8a 1 2 3 4 5 6 LED +6.0000 +3.0000 −3.0000 −6.0000 −3.0000 +3.0000+10.0000 +10.0000 +10.0000 +10.0000 +10.0000 +10.0000 +0.0000 +5.1962+5.1962 +0.0000 −5.1962 −5.1962 PSDpos +23.0000 +11.5000 −11.5000−23.0000 −11.5000 +11.5000 +0.0000 +0.0000 +0.0000 +0.0000 +0.0000+0.0000 +0.0000 +19.9186 +19.9186 +0.0000 −19.9186 −19.9186 PSDdir+0.0000 −0.8660 +0.0000 +0.0000 +0.0000 +0.8660 +1.0000 +0.0000 +1.0000+0.0000 +1.0000 +0.0000 +0.0000 +0.5000 +0.0000 −1.0000 +0.0000 +0.5000IRISpos +20.0000 +10.0000 −10.0000 −20.0000 −10.0000 +10.0000 +1.8000+0.0000 +1.8000 +0.0000 +1.8000 +0.0000 +0.0000 +17.3205 +17.3205+0.0000 −17.3205 −17.3205 IRISdir +0.0000 +0.0000 −0.8660 +0.0000+0.8660 +0.0000 +0.0000 +1.0000 +0.0000 +1.0000 +0.0000 +1.0000 +1.0000+0.0000 −0.5000 +0.0000 −0.5000 +0.0000

TABLE 8b Translation error 7.3%, rotation error 5.5% U1 U2 U3 U4 U5 U6 X+0.0543 −0.4413 −0.0244 −0.0051 −0.0199 +0.4424 Y +0.2791 −0.0029+0.2712 −0.0032 +0.2726 +0.0035 Z −0.0032 +0.2743 +0.0378 −0.5214−0.0436 +0.2441 A +0.0022 +0.4840 −1.3523 −0.9147 +1.3596 +0.4358 B+0.0003 −0.7801 −0.0007 −0.7851 −0.0028 −0.7883 C +1.5842 +0.7692−0.7872 −0.0151 −0.7694 −0.7668Rules for Design of an Optical 3D SensorGroup Formation

From the individual measuring cells, a complete 3D sensor (pan/zoom 3degrees of freedom, or with 6 degrees of freedom) is to be built. Thebasic rule applies, that with N measuring cells at best an N-dimensionalsensor can be built. The sensor is always seen in a Cartesianco-ordinate system which corresponds to the right hand rule. The aim ofthe following group formation is to create rules using which groups ofmeasuring cells (one or more measuring cells) can capture particulardegrees of freedom in Cartesian space.

1-Group

With the 1-group, a single measuring cell is arranged so thatapproximately only one degree of freedom is captured. The measuring cellcan actually capture no rotation, which can only be measured if it alsocauses a displacement (translation because of rotation, “carrouselmovement”).

Conversely, if the moved optical element (LED, diaphragm or PSD) is inor near the centre of rotation of the sensor, the measuring cell canonly measure a translation. FIG. 10 (LED movable) shows such anarrangement for a pan/zoom sensor, which because of the arrangement cancapture no or almost no rotation. The measuring cell 1 can capture onlymovements along the Y axis. Movements along the X axis are determinedusing the measuring cell 2, whereas the measuring cell 3 is responsiblefor measuring movement along the Z axis. TABLE 10a 1 2 3 LED +4.0000+0.0000 −4.0000 +0.0000 +0.0000 +0.0000 +0.0000 −4.0000 +0.0000 PSDpos+21.0000 +0.0000 −21.0000 +0.0000 +0.0000 +0.0000 +0.0000 −21.0000+0.0000 PSDdir +0.0000 +1.0000 +0.0000 +1.0000 +0.0000 +0.0000 +0.0000+0.0000 −1.0000 IRISpos +18.0000 +0.0000 −18.0000 +0.0000 +0.0000+0.0000 +0.0000 −18.0000 +0.0000 IRISdir +0.0000 +0.0000 +0.0000 +0.0000+1.0000 +1.0000 +1.0000 +0.0000 +0.0000

TABLE 10b Translation error 7.2% U1 U2 U3 X −0.0067 −4.6780 −0.0232 Y−4.6262 +0.0065 −0.0082 Z −0.0047 −0.0176 +4.6369

In the next step, the above 3D sensor (pan/zoom) is changed again.Instead of the LEDs in the centre of rotation, the PSDs are now placedthere. Although it would be possible to place three PSDs in the centreof rotation, only a single PSD is used here, but the single PSD is usedby all three measuring cells (multiple use). Obviously, this cannothappen simultaneously, because the PSD can detect only one intersectionpoint of a light plane. Three intersection points simultaneously resultin an arithmetic mean which cannot usefully be processed further.However, it is possible to interrogate the measuring cells insuccession, to switch the LEDs on at staggered times (without overlap),and to determine the intersection points on the PSD in succession.

In the first step, a 1-group is formed. Using it, the movement along aprincipal axis is determined (here along the X axis). FIG. 11 a showsthe measuring cell.

Movement Vector

In FIG. 11 a, the movement vector for this measuring cell is also drawnin. It indicates what movement of the movable optical element themeasuring cell can capture. All movements perpendicular to the movementvector cannot be captured. The movement vector is given by the vectorproduct of IRISdir×LEDdir. It is thus independent of the orientation ofthe PSD (PSDdir). The orientation of the PSD is important for theworking range of the measuring cell, but not for the measurable movementdirection of the measuring cell.

2-Group

In a 2-group, two measuring cells are combined with each other, so thateach measuring cell can capture up to two movements along the axes (X, Yor Z). It must be possible to distinguish the two movements through thecombination of the two measuring cells. This can be read off on thebasis of the appropriate movement vectors. The movement vectors must notbe equal BEW1≠BEW2, or expressed otherwise the volume of the tetrahedron(cross-product) which is stretched out by the movement vectors should beas great as possible (sufficient condition).|BEW1×BEW2|=MAX>0

For the 2-group, the first measuring cell is combined with anothermeasuring cell. The second measuring cell is attached laterally, so thatthe light plane strikes the PSD at 45°. It is thus able to capture theup and down movements along the Y axis as well as the movements alongthe X axis. The two measuring cells together form a 2-group, since eachmeasuring cell can capture up to 2 degrees of freedom and the individualdegrees of freedom can be uniquely deduced from the combination of thetwo captured movements. This relationship can be seen again later in thecalibration matrix of the complete sensor (pan/zoom). The requirementsfor a 2-group do not make it necessary that a measuring cell capturesonly one movement direction (e.g. here along the X axis). A 2-groupwould also be given if the measuring cell 1 was arranged as the mirrorimage of the measuring cell 2. Such a combination is shown in FIG. 12 b.

The third measuring cell must now capture at least the movement alongthe Z axis. A 1-group could achieve this. However, it can no longer beused here, since the PSD is already positioned along the X axis. Amovement in the Z axis can be captured on the PSD only by a light planewhich is rotated in the X/Z plane. This results in an arrangement of thethird measuring cell in which the LED is displaced (e.g. along the Zaxis) and the light plane falls on the PSD as desired through a rotateddiaphragm. FIG. 11 c (PSD movable) shows a possible arrangement. TABLE11a 1 2 3 LED +0.0000 +18.0000 −18.0000 +18.0000 +18.0000 +18.0000+0.0000 +0.0000 +0.0000 PSDpos +0.0000 +0.0000 +0.0000 +0.0000 +0.0000+0.0000 +0.0000 +0.0000 +0.0000 PSDdir +1.0000 +1.0000 +1.0000 +0.0000+0.0000 +0.0000 +0.0000 +0.0000 +0.0000 IRISpos +0.0000 +6.0000 −6.0000+6.0000 +6.0000 +6.0000 +0.0000 +0.0000 +0.0000 IRISdir +0.0000 +0.0000+0.7071 +0.0000 +0.0000 +0.0000 +1.0000 +1.0000 +0.7071

TABLE 11b Translation error 4.2% U1 U2 U3 X −1 0 0 Y −1 +1 0 Z −2 +1 +1

Table 11b shows the calibration matrix, which because of the groupformation can be very easily interpreted. To determine the movementalong the X axis, only the first measuring cell is responsible. Todetermine this movement, only U1 is required. The voltage U2 (secondmeasuring cell) captures the movement along the X axis in a similar wayto the first measuring cell. The difference between the U2 and U1voltages eliminates the X movement, and only the Y movement is left, andis captured only by the second measuring cell. The third measuring cellactually represents a 3-group, because it can measure translatorymovements along all axes. By using the 2-group which is formed with thefirst two measuring cells, the already known movements along the X and Yaxes can be eliminated. The factor for U1 eliminates the movement alongthe X axis for the first and second measuring cells. Additionally, withthe factor for U2, the movement along the Y axis is computationallyremoved from the third measuring cell. Through the calibration matrix inthe third row, only the movement along the Z axis is left, and ismeasured only by the third measuring cell.

Two further variations are shown in FIGS. 12 a and 12 b. They weredesigned using the same methods as the pan/zoom sensor in FIG. 11 c.They show how, with simple changes, different but equivalent oradvantageous sensors can be developed.

In FIG. 12 a (PSD movable), the third measuring cell has been displacedalong the Z axis and not along the X axis as in the case of the sensorof FIG. 11 c. In FIG. 12 b (PSD movable), the symmetrically arrangedmeasuring cells 1 and 2 form a 2-group.

However, a symmetrical arrangement is not absolutely necessary for groupformation. Instead, its purpose is to obtain a simpler calibrationmatrix, and to construct the working range of the complete sensorsymmetrically. The third measuring cell forms a further 2-group with thefirst 2-group (measuring cells 1 and 2), since the measuring cell cannotcapture the movement along the Y axis. TABLE 12a Translation error 4.2%1 2 3 LED +0.0000 +18.0000 +0.0000 +18.0000 +18.0000 +18.0000 +0.0000+0.0000 +18.0000 PSDpos +0.0000 +0.0000 +0.0000 +0.0000 +0.0000 +0.0000+0.0000 +0.0000 +0.0000 PSDdir +1.0000 +1.0000 +1.0000 +0.0000 +0.0000+0.0000 +0.0000 +0.0000 +0.0000 IRISpos +0.0000 +6.0000 +0.0000 +6.0000+6.0000 +6.0000 +0.0000 +0.0000 +6.0000 IRISdir +0.0000 +0.0000 +0.7071+0.0000 +0.0000 +0.0000 +1.0000 +1.0000 +0.7071 U1 U2 U3 X −1 0 0 Y −1+1 0 Z −2 +1 +1

TABLE 12b Translation error 3.3% 1 2 3 LED −18.0000 +18.0000 +0.0000+18.0000 +18.0000 +18.0000 +0.0000 +0.0000 +0.0000 PSDpos +0.0000+0.0000 +0.0000 +0.0000 +0.0000 +0.0000 +0.0000 +0.0000 +0.0000 PSDdir+1.0000 +1.0000 +1.0000 +0.0000 +0.0000 +0.0000 +0.0000 +0.0000 +0.0000IRISpos −6.0000 +6.0000 +0.0000 +6.0000 +6.0000 +6.0000 +0.0000 +0.0000+0.0000 IRISdir +0.0000 +0.0000 +0.7071 +0.0000 +0.0000 +0.0000 +1.0000+1.0000 +0.7071 U1 U2 U3 X −0.5 −0.5 0 Y −0.5 +0.5 0 Z −0.5 −0.5 +1

The above examples show that numerous arrangements result in a pan/zoomsensor. For the basic functions, whether the diagonally incident lightplane is at 45° or a different angle is not decisive. The angle ofincidence affects the gained resolution and the working range of themovement to be captured. By placing the light plane diagonally (in twodegrees of freedom, rotation about the LEDdir and IRISdir vectors), themeasuring cell can also be used for “unfavourable” movements.

In the case of perpendicular or quasi-perpendicular incident light,these additional possibilities cannot be used.

Design of 3D Sensors with 6 Degrees of Freedom

In a similar way to the case of the pan/zoom sensor, a 3D sensor with 6degrees of freedom is now constructed. The 1-groups are set first. Inthis example, the diaphragms will be the movable optical element. Thediaphragms are positioned on the principal axes to form the 1-groups. InFIG. 13 a, the first three measuring cells are positioned.

The diaphragm of the first measuring cell is positioned on the X axis.This measuring cell can therefore capture exclusively movements alongthe X axis. It is suggested as a partner for a 2-group because themovement along the X axis can be completely calculated from a 2-group.The second measuring cell is positioned similarly. It can measure onlythe movements along the Z axis. So that the third measuring cell alsoforms a 1-group, its diaphragm is placed in the co-ordinate origin. Itcan therefore capture only the movements along the Y axis. With thesethree measuring cells, only the translatory movements are measured. Onceeach measuring cell is responsible for exactly one principal axis, it isonly necessary to arrange the remaining three measuring cells in such away that they can capture the rotational degrees of freedom. FIG. 13 b(diaphragm movable) shows a possible arrangement of all six measuringcells. By forming 1-groups, it is enough to capture each of theremaining rotations by only one measuring cell. TABLE 13a 1 2 3 4 5 6LED +9.0000 −14.0000 +0.0000 +16.0000 −14.0000 −9.0000 +0.0000 +0.0000+0.0000 +0.0000 +0.0000 +0.0000 +14.0000 +9.0000 −14.0000 +14.0000+16.0000 +0.0000 PSDpos +9.0000 +4.0000 +0.0000 +16.0000 +4.0000 −9.0000+0.0000 +0.0000 +0.0000 +0.0000 +0.0000 +0.0000 −4.0000 +9.0000 +4.0000−4.0000 +16.0000 −18.0000 PSDdir +1.0000 +0.0000 +0.0000 +0.0000 +0.0000+1.0000 +0.0000 +0.0000 +1.0000 +1.0000 +1.0000 +0.0000 +0.0000 +1.0000+0.0000 +0.0000 +0.0000 +0.0000 IRISpos +9.0000 +0.0000 +0.0000 +16.0000+0.0000 −9.0000 +0.0000 +0.0000 +0.0000 +0.0000 +0.0000 +0.0000 +0.0000+9.0000 +0.0000 +0.0000 +16.0000 −14.0000 IRISdir +0.0000 +0.0000+1.0000 +1.0000 +0.0000 +0.0000 +1.0000 +1.0000 +0.0000 +0.0000 +0.0000+1.0000 +0.0000 +0.0000 +0.0000 +0.0000 +1.0000 +0.0000

The measuring cell 4 captures the rotation about the Z axis (C value) aswell as the movement along the Y axis. Similarly, the measuring cell 5captures the movement along the Y axis and the rotation about the X axis(A value). The remaining rotation about the Y axis is measured by themeasuring cell 6, which can also capture the movement along the X axis.The result is the following calibration matrix. TABLE 13b Translationerror 4.9%, rotation error 13.6% U1 U2 U3 U4 U5 U6 X +0.7578 +0.0006+0.0105 −0.0055 −0.0025 +0.0015 Y +0.0240 −0.0009 +0.7562 +0.0108+0.0029 −0.0040 Z +0.0235 +0.7756 −0.0105 +0.0058 +0.0032 −0.0012 A+0.0265 −0.0149 +2.6868 +0.0174 −2.7359 +0.0043 B +3.1990 −0.0019+0.0349 −0.0127 −0.0083 −3.1562 C −0.0907 +0.0013 −2.6267 +2.6996−0.0233 +0.0249

The calibration matrix shows the chosen arrangement very clearly. Forinstance, the movement along the X axis can be determined only by thefirst measuring cell (voltage U1), although the measuring cell 6 canalso capture the movement along the X axis. Overall, the calibrationmatrix is very thinly populated. Table 13c shows the calibration matrixwith very small values removed. TABLE 13c U1 U2 U3 U4 U5 U6 X +0.7578 Y+0.7562 Z +0.7756 A +2.6868 −2.7359 B +3.1990 −3.1562 C −2.6267 +2.6996

The errors of the calibration matrix for translation and rotation occurbecause of the linearisation which is applied there. However, because ofthe chosen arrangement, the exact model can also be applied very easily.

2-Group

For the next arrangement, 2-groups are formed immediately. The measuringcells in a 2-group are arranged so that two degrees of freedom of a2-group are captured. In this way, the movable optical element no longerhas to be arranged at the origin or along the principal axis. FIG. 14 ashows the first 2-group, which is responsible for measuring the Y and Cmovements. The two measuring cells can capture the Y and C movements.For a single measuring cell, one movement cannot be distinguished fromthe other. The individual movements can only be unambiguouslydistinguished by combining the measuring cells (into a 2-group).

Because of the lateral displacement of the measuring cell 2 to themeasuring cell 1, the second measuring cell can also capture rotationsabout the X axis (movement A). However, because of the short distance tothe axis, this is not particularly pronounced.

Another 2-group now captures two further degrees of freedom. It ispositioned similarly to the first 2-group, but fitted rotated by 90°.The second 2-group is shown in FIG. 14 b. It can capture the movementsalong the X axis and the rotation about the Y axis (B movement).

A 2-group which can capture the missing movements (Z and A) could bearranged along the Y axis. This could happen with the same arrangementas in the cases of the first two 2-groups. Since this would complicatethe structure, the two remaining degrees of freedom are capturedseparately. Each measuring cell supplements the previously positioned2-groups to form a 3-group. FIG. 14 c (diaphragm movable) shows thewhole arrangement. TABLE 14a 1 2 3 4 5 6 LED −10.0000 +10.0000 +0.0000−6.0000 +6.0000 +10.0000 +0.0000 +0.0000 +0.0000 +0.0000 +0.0000 +0.0000+0.0000 +6.0000 +10.0000 −10.0000 −9.0000 −6.0000 PSDpos +19.0000−19.0000 +0.0000 −6.0000 +6.0000 −19.0000 +0.0000 +0.0000 +0.0000+0.0000 +0.0000 +0.0000 +0.0000 +6.0000 −19.0000 +19.0000 +19.0000−6.0000 PSDdir +0.0000 +0.0000 +1.0000 +1.0000 +0.0000 +0.0000 +1.0000+1.0000 +0.0000 +0.0000 +1.0000 +0.0000 +0.0000 +0.0000 +0.0000 +0.0000+0.0000 +1.0000 IRISpos +14.0000 −14.0000 +0.0000 −6.0000 +6.0000−14.0000 +0.0000 +0.0000 +0.0000 +0.0000 +0.0000 +0.0000 +0.0000 +6.0000−14.0000 +14.0000 +14.0000 −6.0000 IRISdir +0.0000 +0.0000 +0.0000+0.0000 +1.0000 +0.0000 +0.0000 +0.0000 +1.0000 +1.0000 +0.0000 +1.0000+1.0000 +1.0000 +0.0000 +0.0000 +0.0000 +0.0000

The measuring cell 5 captures the A and Y movements. It thus supplementsthe first 2-group (measuring cells 1 and 2—Y/C) to form a 3-group. Theequivalent happens with measuring cell 6, which captures movements Z andB. The second 2-group (measuring cells 3 and 4—X/B) becomes a 3-group,and can measure the movements X, B and Z. TABLE 14b Translation error3.5%, rotation error 6.9% U1 U2 U3 U4 U5 U6 X +0.0009 +0.0023 +0.4112+0.4109 +0.0006 −0.0008 Y +0.5574 +0.4707 +0.0022 +0.0018 −0.1973+0.0001 Z −0.0022 −0.0053 +0.4000 −0.4204 −0.0008 +0.8269 A +2.7614+1.1029 −0.0142 −0.0107 −3.8144 +0.0015 B +0.0036 +0.0080 −1.6638+1.7092 −0.0022 +0.0010 C +1.1318 −1.9144 +0.0175 +0.0236 +0.7913+0.00633-Group

In FIG. 15 (diaphragm movable), an arrangement consisting of two3-groups is shown. The first 3-group consisting of measuring cells 1, 3and 5 measures the movements Y, A and B. The remaining movements X, Zand C are captured by the measuring cells 2, 4 and 6. TABLE 15a 1 2 3 45 6 LED −19.9186 −19.9186 +0.0000 +19.9186 +19.9186 =0.0000 +0.0000+0.0000 +0.0000 +0.0000 +0.0000 +0.0000 +11.5000 −11.5000 −23.0000−11.5000 +11.5000 +23.0000 PSDpos +23.0000 +11.5000 −11.5000 −23.0000−11.5000 +11.5000 +0.0000 +0.0000 +0.0000 +0.0000 +0.0000 +0.0000+0.0000 +19.9186 +19.9186 +0.0000 −19.9186 −19.9186 PSDdir +0.0000+0.7071 +0.0000 +0.2588 +0.0000 −0.9659 +1.0000 +0.0000 +1.0000 +0.0000+1.0000 +0.0000 +0.0000 −0.7071 +0.0000 +0.9659 +0.0000 −0.2588 IRISpos+17.4019 +7.4019 −10.0000 −17.4019 −7.4019 +10.0000 +0.0000 +0.0000+0.0000 +0.0000 +0.0000 +0.0000 +1.5000 +15.8205 +14.3205 −1.5000−15.8205 −14.3205 IRISdir −0.2588 +0.0000 +0.9659 +0.0000 −0.7071+0.0000 +0.0000 +1.0000 +0.0000 +1.0000 +0.0000 +1.0000 −0.9659 +0.0000+0.2588 +0.0000 +0.7071 +0.0000

TABLE 15b Translation error 3.0%, rotation error 3.0% U1 U2 U3 U4 U5 U6X +0.0020 +0.4049 +0.0012 +0.1488 +0.0015 −0.5530 Y +0.2901 +0.0031+0.2901 +0.0012 +0.2895 −0.0043 Z −0.0023 −0.4104 −0.0024 +0.5591−0.0016 −0.1487 A −0.1633 −0.0101 −1.5511 −0.0062 +1.7192 +0.0122 B+0.0002 +1.0107 +0.0003 +1.0110 −0.0004 +1.0111 C +1.8993 +0.0007−1.0899 +0.0039 −0.7990 +0.0007

Starting from the above arrangement, two measuring cells are nowcombined. The two LEDs throw the light onto the same PSD. In otherwords, the PSDs of the two measuring cells are in the same place andhave the same orientation. Thus one of the two PSDs is saved. The PSD isusually the most expensive optical element of the measuring cell.

For the calculations, two individual PSDs are still assumed. Thearrangement is changed so that an adjacent LED shines on the PSD of theneighbour. So that the two light planes cause one intersection point onthe PSD, the two PSDs are rotated. The two PSDs thus have the sameorientation, which is rotated at 45° to both light planes. The lightplanes of the two measuring cells are at right angles to each other. Thediaphragm is the movable optical element. It is arranged so that the LEDof the partner measuring cell cannot throw its light plane onto the PSDthrough the wrong slotted diaphragm. The partner slotted diaphragm(“wrong slotted diaphragm”) is arranged so that the diaphragm isarranged in the direction of the partner LED and thus no light incidenceis possible. The diaphragm uses the degree of freedom (see “Changes withno functional effect on the measuring cell”) on the one hand to be thecorrect slotted diaphragm for its own LED, and on the other hand tostand along the direction of the partner LED and thus shade the light.The diaphragm can be extended at the end, to ensure that no externallight from a LED falls on the PSD. FIGS. 16 a to 16 c show a possiblearrangement.

The measuring cells 1, 3, 5 and the measuring cells 2, 4, 6 each form a3-group. The movements X, Z and C are captured using the measuring cells1, 3, 5. The measuring cells 2, 4, 6 are responsible for the movementsY, A and B. FIG. 17 a (diaphragm movable) shows the correspondingarrangement, and in FIG. 17 b the arrangement is shown with one activeLED in each case. TABLE 17a 1 2 3 4 5 6 LED −13.8564 −13.8564 +0.0000+13.8564 +13.8564 +0.0000 +0.0000 +0.0000 +0.0000 +0.0000 +0.0000+0.0000 +8.0000 −8.0000 −16.0000 −8.0000 +8.0000 +16.0000 PSDpos +8.0000+8.0000 +8.0000 −16.0000 −16.0000 +8.0000 +0.0000 +0.0000 +0.0000+0.0000 +0.0000 +0.0000 −13.8564 +13.8564 +13.8564 +0.0000 +0.0000−13.8564 PSDdir −0.6124 −0.6124 +0.6124 +0.0000 +0.0000 +0.6124 +0.7071−0.7071 +0.7071 −0.7071 +0.7071 −0.7071 −0.3536 +0.3536 −0.3536 −0.7071+0.7071 +0.3536 IRISpos +5.2679 +5.2679 +7.000 −12.2679 −12.2679 +7.0000+0.0000 +0.0000 +0.0000 +0.0000 +0.0000 +0.0000 −11.1244 +11.1244+10.1244 −1.0000 +1.0000 −10.1244 IRISdir −0.1736 +0.0000 +0.7660+0.0000 +0.9397 +0.0000 +0.0000 −1.0000 +0.0000 −1.0000 +0.0000 −1.0000+0.9848 +0.0000 +0.6428 +0.0000 −0.3420 +0.0000

TABLE 17b Translation error 10.7%, rotation error 9.5% U1 U2 U3 U4 U5 U6X +0.0039 −0.2769 +0.0023 −0.1024 −0.0025 +0.3785 Y +0.2059 −0.0074+0.2017 −0.0054 +0.1989 +0.0081 Z −0.0017 +0.2849 −0.0021 −0.3834−0.0023 +0.0971 A +1.7543 −0.0133 −1.5713 −0.0174 −0.1600 +0.0112 B−0.0016 −0.9864 +0.0066 −0.9806 −0.0046 −0.9682 C +0.8197 −0.0179+1.0679 −0.0176 −1.8984 +0.0040

An identically functioning 3D sensor can be obtained if all PSDs arerotated about the appropriate LEDdir vector with the same angle. Theslotted diaphragms must be rotated correspondingly, so that the lightplanes again fall on the PSDs rotated by 45° (or a similar angle) andform measurable intersection points.

Further Variations for Arranging Measuring Cells

Co-Ordinate Transformation

The individual measuring cells are arranged in a specified Cartesianco-ordinate system. However, the definition of a co-ordinate system isarbitrary. The relationship between two co-ordinate systems is describedby a linear co-ordinate transformation. The mapping ensures that themagnitude ratios are unchanged and the relationship of the elements toeach other remains the same. Thus for a 3D sensor with 6 degrees offreedom, the co-ordinate system which is used can be arbitrarily definedin space. A 3D sensor can therefore be considered as equivalent if theco-ordinate system which is used can be transferred to a co-ordinatesystem described here using a linear co-ordinate transformation.

Different Movable Optical Elements

To operate a measuring cell, as well as the fixed optical elements amovable element is also required. In all previous arrangements, it isalways assumed that this is of the same type (LED, diaphragm or PSD).Obviously, measuring cells with different movable elements can also becombined with each other. For instance, measuring cells can be arrangedwith movable diaphragms and movable PSDs. The above rules for arranging3D sensors remain valid in this case.

Jointly Used Slotted Diaphragm

The movement which can be captured by a measuring cell is described bythe movement vector, which is calculated from the productIRISdir×LEDdir. From this it can be seen that with one slotted diaphragmtwo different movement vectors can be formed, if the directions of thetwo LEDs are different.

Carrying Signals Via the Springs

It is possible to connect the movable optical element and the two fixedoptical elements via wire springs. This connection can also be used forelectrical cabling of movable and fixed parts of the sensor. Thus aswell as a power supply various control signals can be carried. If theLEDs are the movable optical elements, they can be operated via thesprings, for instance in a matrix arrangement.

Movable LEDs to Extend the Working Range

From the equations of “Calculation of a translatory movement”, anotherinteresting property becomes clear, and experience confirms it. In thecase of a measuring cell with a movable LED, the working range of themovable optical element can be influenced by the arrangement of thefixed optical elements.

In Equation 1 (LED movable), the distance vector PSD-diaphragm isrelated to the distance vector LED-diaphragm. If the diaphragm ispositioned nearer to the PSD than to the LED, this enlarges the movementrange of the LED. In the reverse case, the movement range of the LED isrestricted, but the smaller movement range is then more finely resolved.

In Equation 2 (diaphragm movable), the distance vector LED-PSD isrelated to LED-diaphragm. Since the diaphragm must always be in front ofthe PSD, the distance LED-PSD is always greater than the distanceLED-diaphragm. Therefore, in the case of a movable diaphragm, the resultcan only be a restriction of the movement range.

In Equation 3 (PSD movable), the distance vector LED-diaphragm is inboth the numerator and the denominator. The movement range of the PSD isthus always equal, and corresponds to the maximum extent of thelight-sensitive part of the PSD.

3D Sensor with More Than 6 Measuring Cells

To construct a 3D sensor with 6 degrees of freedom, at least 6 measuringcells are necessary. Obviously, more measuring cells than would actuallybe required can be used. This redundancy of the 3D sensor can be used toincrease the precision of the sensor or to keep the sensor in operationeven if one or more measuring cells fail. This applies equivalently to apan/zoom sensor.

Appendix A

Example Calculation

Appendix B

In this embodiment of the invention, which is illustrated in FIG. 22,only the LEDs are movable, and they are in or near the centre ofrotation. The measuring cells can therefore capture translatorymovements only, and are “blind” for rotational movements.

The sensor structure is therefore suitable only for pan/zoomapplications, and not for applications with 6 degrees of freedom (6DOF). The design aim for a pan/zoom sensor is therefore to relocate themovable element into the centre of rotation.

In this description, if it is said that a measuring cell can capture“generally only” or “exclusively” translatory movements, this means thatthe measuring cell or sensor can measure exclusively translatorymovements, at least in a first approximation. Rotational movements canalso have a small influence on the measurement. This part is small andtherefore negligible, but nevertheless present. The result of thedisplacement and rotation of the sensor is that in the sensor theindividual measuring cells slightly leave their ideal positions (e.g.the movable element is no longer exactly in the centre of rotation), sothat small errors occur.

This situation is handled using the following method:

Method of determining relative movements or relative positions of twoobjects in an arrangement according to the invention, which can capturetranslatory and rotational movements or generally translatory movementsonly, with the steps:

-   -   one specifies the exact equations for the captured movements of        the measuring cells; (see page 13 from line 1)    -   one specifies a first approximation, which ignores the coupled        movements between rotation and/or translation; (see page 14 from        line 17) or    -   for each measuring cell, one specifies the calibration matrix of        the linearisation and the maximum error.

REFERENCE SYMBOL LIST

-   101 LED-   102 light cone-   103 diaphragm-   104 light plane-   105 PSD-   301 light plane-   302 PSD-   303 intersection plane-   304 intersection point-   401 PSD-   402 diaphragm-   403 diaphragm distance-   404 displacement X-   405 displacement Y-   406 LED-   1001 measuring cell 1-   1002 measuring cell 2-   1003 measuring cell 3-   1100 measuring cell 1-   1101 movement vector 1-   1102 measuring cell 2-   1103 movement vector 2-   1104 measuring cell 3-   1105 movement vector 3-   1300 measuring cell 1-   1301 measuring cell 2-   1302 measuring cell 3-   1303 measuring cell 4-   1304 measuring cell 5-   1305 measuring cell 6-   1400 measuring cell 1-   1401 measuring cell 2-   1402 measuring cell 3-   1403 measuring cell 4-   1404 measuring cell 4-   1405 measuring cell 5-   1500 measuring cell 1-   1501 measuring cell 2-   1502 measuring cell 3-   1503 measuring cell 4-   1504 measuring cell 5-   1505 measuring cell 6-   1700 measuring cell 1-   1701 measuring cell 2-   1702 measuring cell 3-   1703 measuring cell 4-   1704 measuring cell 5-   1705 measuring cell 6-   1710 no LED active-   1711 LED 1 active-   1712 LED 2 active-   1713 LED 3 active-   1714 LED 4 active-   1715 LED 5 active-   1716 LED 6 active-   1800 1900 2000 2100 LED-   1801 1901 2001 2101 diaphragm-   1802 1902 2002 2102 PSD-   2200 measuring cell 1-   2201 measuring cell 2-   2202 measuring cell 3

1. Opto-electronic arrangement to capture relative movements or relativepositions of two objects, including at least one position-sensitivedetector, characterized in that the position-sensitive detector isilluminated by at least two light emission devices, to form twomeasuring cells with a common detector.
 2. Opto-electronic arrangementaccording to claim 1, characterized in that each of the two measuringcells which are formed by a common detector has a slotted diaphragmwhich is arranged in the beam path of the corresponding light emissiondevice, between the said light emission device and theposition-sensitive detector.
 3. Opto-electronic arrangement according toclaim 2, wherein each position-sensitive detector is functionallyassociated with two adjacent slotted diaphragms.
 4. Opto-electronicarrangement according to claim 2, characterized in that a slot directionof at least one of the slotted diaphragms is aligned diagonally inrelation to the light-sensitive part of the detector.
 5. Opto-electronicarrangement according to claim 2, characterized in that a light plane,which shines through at least one of the slotted diaphragms and falls onthe detector, encloses an acute angle with a plane of a light-sensitivepart of the detector.
 6. Opto-electronic arrangement according to claim1, characterized in that each detector is illuminated alternately by alight emission device, a measurement value of the detector being readout simultaneously.
 7. Opto-electronic arrangement according to claim 6,characterized in that the detector of each measuring cell is illuminatedby only one light emission device at a particular time, and themeasurement value of the detector is read out simultaneously. 8.Opto-electronic arrangement according to claim 1, characterized in thatone element of each measuring cell, consisting of light emission device,slotted diaphragm and detector, is movable relative to the other twoelements.
 9. Opto-electronic arrangement according to claim 8,characterized in that the movable element is arranged in the centre ofrotation of the measuring cell, so that the measuring cell can mainlycapture only translatory movements.
 10. Opto-electronic arrangement tocapture relative movements or relative positions of two objects,including at least one position-sensitive detector, theposition-sensitive detector being illuminated by a light emissiondevice, to form a measuring cell, which also has a slotted diaphragmwhich is arranged in the beam path of the light emission device betweenthe light emission device and the position-sensitive detector,characterized in that a light plane which shines through the slotteddiaphragm and falls on the detector is oriented at an angle in relationto a light-sensitive part of the detector.
 11. Opto-electronicarrangement according to claim 10, characterized in that a slotdirection of the slotted diaphragm is aligned diagonally in relation tothe light-sensitive part of the detector.
 12. Opto-electronicarrangement according to claim 10, characterized in that the light planeencloses an acute angle with a plane of the light-sensitive part of thedetector.
 13. Opto-electronic arrangement according to claim 12,characterized in that a slot direction of the slotted diaphragm runsessentially perpendicularly to the light-sensitive part of the detector.14. Opto-electronic arrangement according to claim 10, characterized inthat one element of each measuring cell, consisting of light emissiondevice, slotted diaphragm and detector, is movable relative to the othertwo elements.
 15. Opto-electronic arrangement according to claim 14,characterized in that the movable element is arranged in the centre ofrotation of the measuring cell, so that the measuring cell can captureexclusively translatory movements.
 16. Opto-electronic arrangementaccording to claim 10, characterized in that the position-sensitivedetector is associated with two slotted diaphragms, saidposition-sensitive detector acting as part of two different measuringcells.
 17. Opto-electronic arrangement according to claim 16,characterized in that the said two slotted diaphragms are adjacent. 18.Opto-electronic arrangement according to claim 17, characterized in thateach of the two adjacent slotted diaphragms is illuminated by a lightemission device which is arranged for it.
 19. Opto-electronicarrangement according to claim 17, characterized in that the twoadjacent slotted diaphragms have slots which are arrangedperpendicularly to each other.
 20. Opto-electronic arrangement accordingto claim 17, characterized in that the two adjacent slotted diaphragmsenclose an angle together.
 21. Opto-electronic arrangement according toclaim 17, characterized in that each slotted diaphragm is illuminated byits own light emission device, so that each position-sensitive detectoris illuminated by two light emission devices; to form one measuring cellwith a common detector.
 22. Opto-electronic arrangement to capturerelative movements or relative positions of two objects, including atleast one position-sensitive detector, each position-sensitive detectorbeing illuminated by its own light emission device, to form a measuringcell, characterized in that the measuring cells are arranged in groups,so that the measuring cells of each group are essentially arrangedparallel or perpendicularly to each other.
 23. Opto-electronicarrangement according to claim 22, characterized in that the measuringcells are arranged in a common plane.
 24. Opto-electronic arrangementaccording to claim 22, characterized in that the measuring cells alsoeach include a slotted diaphragm which is arranged in the beam path ofthe light emission device between the light emission device and theposition-sensitive detector, a detector axis of the position-sensitivedetector being aligned essentially perpendicularly to a slot directionof the slotted diaphragm.
 25. Opto-electronic arrangement according toclaim 22, characterized in that the detector axes of the twoposition-sensitive detectors in a group of two measuring cells areessentially arranged parallel to each other.
 26. Opto-electronicarrangement according to claim 22, characterized in that the detectoraxes of the two position-sensitive detectors in a group of two measuringcells are essentially arranged perpendicularly to each other. 27.Opto-electronic arrangement according to claim 22, characterized in thatone element of each measuring cell, consisting of light emission device,slotted diaphragm and detector, is movable relative to the other twoelements.
 28. Opto-electronic arrangement according to claim 27,characterized in that the movable element is arranged in the centre ofrotation of the measuring cell, so that the measuring cell can mainlycapture only translatory movements.
 29. Opto-electronic arrangement tocapture relative movements or relative positions of two objects,including at least two position-sensitive detectors, eachposition-sensitive detector being illuminated by a light emissiondevice, to form a measuring cell, characterized in that theposition-sensitive detectors and light emission devices are arranged ina common plane, and that the measuring cells are arranged parallel toCartesian axes.
 30. Opto-electronic arrangement according to claim 29,characterized in that the two measuring cells are arranged essentiallyparallel to each other.
 31. Opto-electronic arrangement according toclaim 29, characterized in that the two measuring cells are arrangedessentially perpendicularly to each other.
 32. Opto-electronicarrangement according to claim 29, characterized in that the measuringcells also each include a slotted diaphragm which is arranged in thebeam path of the light emission device between the light emission deviceand the position-sensitive detector, a detector axis of theposition-sensitive detector being aligned essentially perpendicularly toa slot direction of the slotted diaphragm.
 33. Opto-electronicarrangement according to claim 29, characterized in that one element ofeach measuring cell, consisting of light emission device, slotteddiaphragm and detector, is movable relative to the other two elements.34. Opto-electronic arrangement according to claim 33, characterized inthat the movable element is arranged in the centre of rotation of themeasuring cell, so that the measuring cell can capture exclusivelytranslatory movements.
 35. Opto-electronic arrangement to capturerelative movements or relative positions of two objects, including atleast one position-sensitive detector, each position-sensitive detectorbeing illuminated by a light emission device, to form a measuring cell,and the measuring cell also having a slotted diaphragm which is arrangedin the beam path of the light emission device between the light emissiondevice and the position-sensitive detector, an element of the measuringcell, consisting of light emission device, slotted diaphragm anddetector, being movable relative to the other two elements,characterized in that the measuring cell can capture exclusivelytranslatory movements.
 36. Opto-electronic arrangement according toclaim 35, characterized in that the movable element of the measuringcell is arranged in the centre of rotation of the measuring cell. 37.Opto-electronic arrangement according to claim 35, characterized in thatthe movable element of each measuring cell is arranged in the centre ofrotation of the appropriate measuring cell.
 38. Opto-electronicarrangement according to claim 1, characterized in that the arrangementincludes at least three measuring cells.
 39. Opto-electronic arrangementaccording to claim 38, characterized in that the arrangement includesmore than six measuring cells.
 40. Opto-electronic arrangement accordingto claim 1, characterized in that the measuring cell consisting of lightemission device, slotted diaphragm and detector is provided with amovable light emission device, this measuring cell having a greaterworking range or movement range.
 41. Opto-electronic arrangementaccording to claim 1, characterized in that each element of eachmeasuring cell consisting of light emission device, slotted diaphragmand detector can be arranged to be movable relative to the other twoelements.
 42. Force and/or moment sensor, characterized by anopto-electronic arrangement to capture relative movements or relativepositions of two objects according to claim
 1. 43. Force and/or momentsensor according to claim 42, characterized in that the two objectsconsist of a first plate and a second plate, which are elasticallyjoined to each other and movable relative to each other.
 44. Forceand/or moment sensor according to claim 43, characterized in that thefirst and second plates are joined to each other via at least one springdevice and/or damping device.
 45. Force and/or moment sensor accordingto claim 44, characterized in that a spring, as well as the dampingproperty, can simultaneously be used to carry electrical signals of thetwo movable plates.
 46. Force and/or moment sensor according to claim44, characterized in that the at least one spring device and/or dampingdevice includes one of the following components or combinations of them:helical spring, spring assembly, elastomer, cast resin.
 47. Force and/ormoment sensor according to claim 44, characterized in that the springdevices and/or damping devices are essentially arranged with rotationalsymmetry.
 48. Force and/or moment sensor according to claim 44,characterized in that at least one of the spring devices and/or dampingdevices includes at least one elastomer element or spring element, whichis permanently joined to the first and second plates.
 49. Force and/ormoment sensor according to claim 43, characterized by at least one limitstop device, which limits the movement of the first plate relative tothe second plate.
 50. Force and/or moment sensor according to claim 42,characterized in that the sensor can capture exclusively translatorymovements.
 51. Pan/zoom sensor with a first plate and a second plate,which are elastically joined to each other and movable relative to eachother, characterized by an opto-electronic arrangement to capturerelative movements or relative positions of two objects according toclaim
 1. 52. Pan/zoom sensor according to claim 51, the sensor beingable to capture exclusively translatory movements because of itsgeometrical structure.
 53. PC keyboard, characterized in that it has asensor according to claim
 42. 54. A method of determining relativemovements or relative positions of two objects in an opto-electronicarrangement or relative positions of two objects, including at least oneposition-sensitive detector, characterized in that theposition-sensitive detector is illuminated by at least two lightemission devices, to form two measuring cells with a common detector,which can capture translatory and rotational movements or mainlytranslatory movements only, by one of: specifying the exact equationsfor the relative movements of the measuring cells; specifying a firstapproximation, which ignores the coupled movements between rotationand/or translation; and specifying the linearisation and maximum errorvia the calibration matrix.